1.Suppose we observe the following relationship between income and utility for John: Income/Utility: 20,000 50 25,000 65 27,000 70 30,000 75 35,000 83 40,000 90 a) Roughly sketch this utility function. Why does it have this shape? b) Explain in what sense can John be considered risk-averse? c) Suppose that John’s current income is $40,000. The probability of illness is 0.5, in which case he incurs medical expenses of $20,000. What is John’s expected income and expected utility? d) What is John’s loss of utility due to this uncertainty? e) What is the maximum premium that John will pay for insurance of $20,000? f) What is the actuarially fair premium for John? Based on (e), what is John’s risk premium? g) Suppose that the premium rate charged to John is 50 cents for each dollar of coverage. How much coverage (what dollar amount) will John buy in this case? 2. In class, we say that an individual will choose the optimal level (quantity) of insurance coverage by comparing the marginal benefits (MB) and the marginal costs (MC) of additional insurance. Suppose that John is
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